The volumetric distribution of valuable mineral, or phase, within a set of
particles is called the liberation distribution. To optimise a mineral
processing plant it is necessary to know the liberation distribution in most
of the streams, especially those adjacent to separation devices. Possibly the most common method of analysing ore particles is to
section sets of similarly-sized particles. However, the observed sections
can appear liberated even if the particle is composite. This means that the
'apparent' liberation distribution can be very different to the 'actual'
liberation distribution. This discrepancy is called stereological error. One must then somehow estimate the actual liberation distribution
using the apparent liberation distribution. This problem is called the
liberation distribution problem and its solution is the subject of this paper. The solution is based on a sorting algorithm which uses geometric
probability equations. These equations are based on the assumption that
sectioning is isotropic and uniform. Apart from these assumptions the
equations are completely independent of particle shape or texture. The algorithm is verified by numerical simulation and experimental
methods. For the numerical simulations the correspondence between the
actual and estimated liberation distributions is excellent. For the
experimental methods, the agreement is not as good and appears to be due
to experimental errors.